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in how many ways can 9 identical balls be distributed among four baske
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17 Mar 2018, 03:28
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Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball? A. 35 B. 56 C. 63 D. 70 E. 126 Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance
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in how many ways can 9 identical balls be distributed among four baske
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17 Mar 2018, 05:08
rishabhmishra wrote: Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball? A. 35 B. 56 C. 63 D. 70 E. 126 Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance This question is based on Distribution principle. It can be done in two ways This is like find total Natural number solution of an equation a+b+c+d = 9 Method 1: Natural Number solution of an equation in r variables = (n1)C(r1) = (91)C(41) = 8C3 = 56 Method 2: Assign one ball to each basket i.e. 4 balls are gone and we are left with only 5 balls to assign to the baskets Now every basket needs balls from 0 to 5 a+b+c+d = 5 and a, b, c and d may be any integer from 0 to 5 Now manually find solutions which is long but you get a pattern in that as well leading you to the answer i,e, 56 Answer: option B
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Re: in how many ways can 9 identical balls be distributed among four baske
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17 Mar 2018, 12:20
rishabhmishra wrote: Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball? A. 35 B. 56 C. 63 D. 70 E. 126 Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance If we were to manually list down all the possibilities for the four baskets(and the 4 digit number is the total number of balls in the basket number one, two, three, and four) 6111 (4 ways)  6111,1611,1161,1116 3222 (4 ways)  3222,2322,2232,2223 4221 (12 ways)  4221,4212,4122,2124,2142,2421,2412,2241,2214,1224,1242,1422 4311 (12 ways)  4311,4131,4113,3411,3114,3141,1341,1431,1143,1134,1413,1314 1233 (12 ways)  1233,1323,1332,2133,2331,2313,3321,3231,3123,3132,3312,3213 5112 (12 ways)  5112,5121,5211,2511,2151,2115,1215,1251,1125,1152,1521,1512Therefore, there are \(4*2 + 12*4\) or 56 ways(Option B) in which the 9 balls can be arranged among the 4 baskets.
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Re: in how many ways can 9 identical balls be distributed among four baske
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17 Mar 2018, 22:45
rishabhmishra wrote: Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball? A. 35 B. 56 C. 63 D. 70 E. 126 Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance hi.. the question does NOT mention about the baskets, if they too are identical.. 1) Identical boxes..a) 6,1,1,1 b) 5,2,1,1 c) 4,3,1,1 d) 4,2,2,1 e) 3,3,2,1 f) 3,2,2,2 so 6 ways 2) non identical boxes..a) 6,1,1,1 ............. \(\frac{4!}{3!} = 4\) b) 5,2,1,1............. \(\frac{4!}{2!} = 4*3=12\) c) 4,3,1,1............. \(\frac{4!}{2!} = 4*3=12\) d) 4,2,2,1............. \(\frac{4!}{2!} = 4*3=12\) e) 3,3,2,1............. \(\frac{4!}{2!} = 4*3=12\) f) 3,2,2,2............. \(\frac{4!}{3!} = 4\) so 4+12+12+12+12+4=56 In these cases we can take it as an equation a+b+c+d=9, as shown above.. For other type of such possible scenarios https://gmatclub.com/forum/topic215915.html
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Re: in how many ways can 9 identical balls be distributed among four baske
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18 Mar 2018, 20:14
chetan2uIf we remove the last condition i.e. such that each basket gets at least one ball. The possible combination  9!^4 am I correct?



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Re: in how many ways can 9 identical balls be distributed among four baske
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14 Jun 2019, 11:11
GMATinsight wrote: rishabhmishra wrote: Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball? A. 35 B. 56 C. 63 D. 70 E. 126 Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance This question is based on Distribution principle. It can be done in two ways This is like find total Natural number solution of an equation a+b+c+d = 9 Method 1: Natural Number solution of an equation in r variables = (n1)C(r1) = (91)C(41) = 8C3 = 56 Method 2: Assign one ball to each basket i.e. 4 balls are gone and we are left with only 5 balls to assign to the baskets Now every basket needs balls from 0 to 5 a+b+c+d = 5 and a, b, c and d may be any integer from 0 to 5 Now manually find solutions which is long but you get a pattern in that as well leading you to the answer i,e, 56 Answer: option B Could you please explain what "natural number solution" means? How would the approach change if the numbers changed? e.g. if 10 identical balls were distributed among 4 boxes and each box gets at least 2 balls, in how many ways could the balls be distributed? Posted from my mobile device



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Re: in how many ways can 9 identical balls be distributed among four baske
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16 Aug 2019, 11:14
rishabhmishra wrote: Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball? A. 35 B. 56 C. 63 D. 70 E. 126 Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance As Baskets are 4, solution should be a multiple of 4. Instead of calculating it the long way, we can use Triage in this question. Only solution multiple of 4 is B. Hence the Answer.



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Re: in how many ways can 9 identical balls be distributed among four baske
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16 Aug 2019, 11:25
Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball? A. 35 B. 56 C. 63 D. 70 E. 126
Correct Answere is B



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Re: in how many ways can 9 identical balls be distributed among four baske
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18 Aug 2019, 23:07
Anuragjn reasoning seems wrong to me, as we are summing different numbers of 4 baskets (not multiplying), so not necessarily divisible by 4 Can someone please explain? Is this question within scope of gmat?




Re: in how many ways can 9 identical balls be distributed among four baske
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18 Aug 2019, 23:07






